Properties

Label 8041.2.a.g.1.4
Level 8041
Weight 2
Character 8041.1
Self dual yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.67122 q^{2} +2.62074 q^{3} +5.13539 q^{4} +0.949400 q^{5} -7.00056 q^{6} -4.03564 q^{7} -8.37532 q^{8} +3.86827 q^{9} +O(q^{10})\) \(q-2.67122 q^{2} +2.62074 q^{3} +5.13539 q^{4} +0.949400 q^{5} -7.00056 q^{6} -4.03564 q^{7} -8.37532 q^{8} +3.86827 q^{9} -2.53605 q^{10} -1.00000 q^{11} +13.4585 q^{12} +0.167776 q^{13} +10.7801 q^{14} +2.48813 q^{15} +12.1015 q^{16} +1.00000 q^{17} -10.3330 q^{18} -8.43016 q^{19} +4.87554 q^{20} -10.5764 q^{21} +2.67122 q^{22} +5.22814 q^{23} -21.9495 q^{24} -4.09864 q^{25} -0.448166 q^{26} +2.27550 q^{27} -20.7246 q^{28} +8.85167 q^{29} -6.64633 q^{30} +5.94666 q^{31} -15.5751 q^{32} -2.62074 q^{33} -2.67122 q^{34} -3.83144 q^{35} +19.8651 q^{36} +5.66287 q^{37} +22.5188 q^{38} +0.439697 q^{39} -7.95152 q^{40} -1.71029 q^{41} +28.2517 q^{42} +1.00000 q^{43} -5.13539 q^{44} +3.67253 q^{45} -13.9655 q^{46} +2.40992 q^{47} +31.7148 q^{48} +9.28639 q^{49} +10.9484 q^{50} +2.62074 q^{51} +0.861596 q^{52} -7.83596 q^{53} -6.07835 q^{54} -0.949400 q^{55} +33.7998 q^{56} -22.0932 q^{57} -23.6447 q^{58} -9.07751 q^{59} +12.7775 q^{60} +6.13333 q^{61} -15.8848 q^{62} -15.6109 q^{63} +17.4014 q^{64} +0.159287 q^{65} +7.00056 q^{66} -4.24323 q^{67} +5.13539 q^{68} +13.7016 q^{69} +10.2346 q^{70} -11.5783 q^{71} -32.3980 q^{72} +4.99497 q^{73} -15.1267 q^{74} -10.7415 q^{75} -43.2922 q^{76} +4.03564 q^{77} -1.17453 q^{78} +4.03713 q^{79} +11.4892 q^{80} -5.64131 q^{81} +4.56855 q^{82} -7.69890 q^{83} -54.3137 q^{84} +0.949400 q^{85} -2.67122 q^{86} +23.1979 q^{87} +8.37532 q^{88} +3.38193 q^{89} -9.81013 q^{90} -0.677084 q^{91} +26.8486 q^{92} +15.5846 q^{93} -6.43741 q^{94} -8.00359 q^{95} -40.8181 q^{96} -6.26604 q^{97} -24.8059 q^{98} -3.86827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67122 −1.88883 −0.944417 0.328749i \(-0.893373\pi\)
−0.944417 + 0.328749i \(0.893373\pi\)
\(3\) 2.62074 1.51308 0.756542 0.653945i \(-0.226887\pi\)
0.756542 + 0.653945i \(0.226887\pi\)
\(4\) 5.13539 2.56770
\(5\) 0.949400 0.424585 0.212292 0.977206i \(-0.431907\pi\)
0.212292 + 0.977206i \(0.431907\pi\)
\(6\) −7.00056 −2.85797
\(7\) −4.03564 −1.52533 −0.762664 0.646795i \(-0.776109\pi\)
−0.762664 + 0.646795i \(0.776109\pi\)
\(8\) −8.37532 −2.96112
\(9\) 3.86827 1.28942
\(10\) −2.53605 −0.801970
\(11\) −1.00000 −0.301511
\(12\) 13.4585 3.88514
\(13\) 0.167776 0.0465327 0.0232664 0.999729i \(-0.492593\pi\)
0.0232664 + 0.999729i \(0.492593\pi\)
\(14\) 10.7801 2.88109
\(15\) 2.48813 0.642432
\(16\) 12.1015 3.02537
\(17\) 1.00000 0.242536
\(18\) −10.3330 −2.43551
\(19\) −8.43016 −1.93401 −0.967006 0.254755i \(-0.918005\pi\)
−0.967006 + 0.254755i \(0.918005\pi\)
\(20\) 4.87554 1.09020
\(21\) −10.5764 −2.30795
\(22\) 2.67122 0.569505
\(23\) 5.22814 1.09014 0.545072 0.838389i \(-0.316502\pi\)
0.545072 + 0.838389i \(0.316502\pi\)
\(24\) −21.9495 −4.48042
\(25\) −4.09864 −0.819728
\(26\) −0.448166 −0.0878926
\(27\) 2.27550 0.437920
\(28\) −20.7246 −3.91658
\(29\) 8.85167 1.64371 0.821857 0.569694i \(-0.192938\pi\)
0.821857 + 0.569694i \(0.192938\pi\)
\(30\) −6.64633 −1.21345
\(31\) 5.94666 1.06805 0.534026 0.845468i \(-0.320678\pi\)
0.534026 + 0.845468i \(0.320678\pi\)
\(32\) −15.5751 −2.75331
\(33\) −2.62074 −0.456212
\(34\) −2.67122 −0.458110
\(35\) −3.83144 −0.647631
\(36\) 19.8651 3.31085
\(37\) 5.66287 0.930970 0.465485 0.885056i \(-0.345880\pi\)
0.465485 + 0.885056i \(0.345880\pi\)
\(38\) 22.5188 3.65303
\(39\) 0.439697 0.0704079
\(40\) −7.95152 −1.25725
\(41\) −1.71029 −0.267102 −0.133551 0.991042i \(-0.542638\pi\)
−0.133551 + 0.991042i \(0.542638\pi\)
\(42\) 28.2517 4.35934
\(43\) 1.00000 0.152499
\(44\) −5.13539 −0.774190
\(45\) 3.67253 0.547469
\(46\) −13.9655 −2.05910
\(47\) 2.40992 0.351523 0.175761 0.984433i \(-0.443761\pi\)
0.175761 + 0.984433i \(0.443761\pi\)
\(48\) 31.7148 4.57764
\(49\) 9.28639 1.32663
\(50\) 10.9484 1.54833
\(51\) 2.62074 0.366977
\(52\) 0.861596 0.119482
\(53\) −7.83596 −1.07635 −0.538176 0.842833i \(-0.680886\pi\)
−0.538176 + 0.842833i \(0.680886\pi\)
\(54\) −6.07835 −0.827159
\(55\) −0.949400 −0.128017
\(56\) 33.7998 4.51668
\(57\) −22.0932 −2.92632
\(58\) −23.6447 −3.10470
\(59\) −9.07751 −1.18179 −0.590896 0.806748i \(-0.701225\pi\)
−0.590896 + 0.806748i \(0.701225\pi\)
\(60\) 12.7775 1.64957
\(61\) 6.13333 0.785293 0.392646 0.919690i \(-0.371560\pi\)
0.392646 + 0.919690i \(0.371560\pi\)
\(62\) −15.8848 −2.01737
\(63\) −15.6109 −1.96679
\(64\) 17.4014 2.17517
\(65\) 0.159287 0.0197571
\(66\) 7.00056 0.861709
\(67\) −4.24323 −0.518393 −0.259196 0.965825i \(-0.583458\pi\)
−0.259196 + 0.965825i \(0.583458\pi\)
\(68\) 5.13539 0.622758
\(69\) 13.7016 1.64948
\(70\) 10.2346 1.22327
\(71\) −11.5783 −1.37409 −0.687043 0.726616i \(-0.741092\pi\)
−0.687043 + 0.726616i \(0.741092\pi\)
\(72\) −32.3980 −3.81814
\(73\) 4.99497 0.584617 0.292308 0.956324i \(-0.405577\pi\)
0.292308 + 0.956324i \(0.405577\pi\)
\(74\) −15.1267 −1.75845
\(75\) −10.7415 −1.24032
\(76\) −43.2922 −4.96595
\(77\) 4.03564 0.459904
\(78\) −1.17453 −0.132989
\(79\) 4.03713 0.454212 0.227106 0.973870i \(-0.427074\pi\)
0.227106 + 0.973870i \(0.427074\pi\)
\(80\) 11.4892 1.28453
\(81\) −5.64131 −0.626813
\(82\) 4.56855 0.504512
\(83\) −7.69890 −0.845064 −0.422532 0.906348i \(-0.638859\pi\)
−0.422532 + 0.906348i \(0.638859\pi\)
\(84\) −54.3137 −5.92612
\(85\) 0.949400 0.102977
\(86\) −2.67122 −0.288045
\(87\) 23.1979 2.48708
\(88\) 8.37532 0.892812
\(89\) 3.38193 0.358484 0.179242 0.983805i \(-0.442636\pi\)
0.179242 + 0.983805i \(0.442636\pi\)
\(90\) −9.81013 −1.03408
\(91\) −0.677084 −0.0709777
\(92\) 26.8486 2.79916
\(93\) 15.5846 1.61605
\(94\) −6.43741 −0.663968
\(95\) −8.00359 −0.821151
\(96\) −40.8181 −4.16598
\(97\) −6.26604 −0.636220 −0.318110 0.948054i \(-0.603048\pi\)
−0.318110 + 0.948054i \(0.603048\pi\)
\(98\) −24.8059 −2.50578
\(99\) −3.86827 −0.388775
\(100\) −21.0481 −2.10481
\(101\) 13.5038 1.34367 0.671837 0.740699i \(-0.265505\pi\)
0.671837 + 0.740699i \(0.265505\pi\)
\(102\) −7.00056 −0.693158
\(103\) −19.6363 −1.93482 −0.967410 0.253215i \(-0.918512\pi\)
−0.967410 + 0.253215i \(0.918512\pi\)
\(104\) −1.40518 −0.137789
\(105\) −10.0412 −0.979920
\(106\) 20.9315 2.03305
\(107\) 15.0067 1.45075 0.725374 0.688355i \(-0.241667\pi\)
0.725374 + 0.688355i \(0.241667\pi\)
\(108\) 11.6856 1.12445
\(109\) −18.2609 −1.74907 −0.874537 0.484958i \(-0.838835\pi\)
−0.874537 + 0.484958i \(0.838835\pi\)
\(110\) 2.53605 0.241803
\(111\) 14.8409 1.40864
\(112\) −48.8372 −4.61468
\(113\) −0.831552 −0.0782258 −0.0391129 0.999235i \(-0.512453\pi\)
−0.0391129 + 0.999235i \(0.512453\pi\)
\(114\) 59.0158 5.52734
\(115\) 4.96360 0.462858
\(116\) 45.4568 4.22056
\(117\) 0.649003 0.0600003
\(118\) 24.2480 2.23221
\(119\) −4.03564 −0.369946
\(120\) −20.8389 −1.90232
\(121\) 1.00000 0.0909091
\(122\) −16.3835 −1.48329
\(123\) −4.48222 −0.404148
\(124\) 30.5385 2.74243
\(125\) −8.63825 −0.772628
\(126\) 41.7002 3.71495
\(127\) 10.0286 0.889894 0.444947 0.895557i \(-0.353222\pi\)
0.444947 + 0.895557i \(0.353222\pi\)
\(128\) −15.3327 −1.35523
\(129\) 2.62074 0.230743
\(130\) −0.425489 −0.0373179
\(131\) −18.2205 −1.59194 −0.795968 0.605339i \(-0.793038\pi\)
−0.795968 + 0.605339i \(0.793038\pi\)
\(132\) −13.4585 −1.17141
\(133\) 34.0211 2.95000
\(134\) 11.3346 0.979158
\(135\) 2.16036 0.185934
\(136\) −8.37532 −0.718177
\(137\) −0.803989 −0.0686894 −0.0343447 0.999410i \(-0.510934\pi\)
−0.0343447 + 0.999410i \(0.510934\pi\)
\(138\) −36.5999 −3.11559
\(139\) −18.8259 −1.59679 −0.798397 0.602132i \(-0.794318\pi\)
−0.798397 + 0.602132i \(0.794318\pi\)
\(140\) −19.6759 −1.66292
\(141\) 6.31576 0.531883
\(142\) 30.9280 2.59542
\(143\) −0.167776 −0.0140301
\(144\) 46.8118 3.90098
\(145\) 8.40377 0.697895
\(146\) −13.3426 −1.10424
\(147\) 24.3372 2.00730
\(148\) 29.0811 2.39045
\(149\) 21.8999 1.79411 0.897053 0.441922i \(-0.145703\pi\)
0.897053 + 0.441922i \(0.145703\pi\)
\(150\) 28.6928 2.34275
\(151\) −9.65566 −0.785766 −0.392883 0.919588i \(-0.628522\pi\)
−0.392883 + 0.919588i \(0.628522\pi\)
\(152\) 70.6052 5.72684
\(153\) 3.86827 0.312731
\(154\) −10.7801 −0.868682
\(155\) 5.64576 0.453479
\(156\) 2.25802 0.180786
\(157\) 16.0423 1.28031 0.640156 0.768245i \(-0.278870\pi\)
0.640156 + 0.768245i \(0.278870\pi\)
\(158\) −10.7840 −0.857932
\(159\) −20.5360 −1.62861
\(160\) −14.7870 −1.16901
\(161\) −21.0989 −1.66283
\(162\) 15.0692 1.18395
\(163\) 15.6179 1.22329 0.611643 0.791134i \(-0.290509\pi\)
0.611643 + 0.791134i \(0.290509\pi\)
\(164\) −8.78301 −0.685838
\(165\) −2.48813 −0.193701
\(166\) 20.5654 1.59619
\(167\) 1.52626 0.118105 0.0590526 0.998255i \(-0.481192\pi\)
0.0590526 + 0.998255i \(0.481192\pi\)
\(168\) 88.5803 6.83412
\(169\) −12.9719 −0.997835
\(170\) −2.53605 −0.194506
\(171\) −32.6101 −2.49376
\(172\) 5.13539 0.391570
\(173\) −10.9673 −0.833825 −0.416913 0.908947i \(-0.636888\pi\)
−0.416913 + 0.908947i \(0.636888\pi\)
\(174\) −61.9666 −4.69768
\(175\) 16.5406 1.25035
\(176\) −12.1015 −0.912184
\(177\) −23.7898 −1.78815
\(178\) −9.03386 −0.677117
\(179\) −16.9601 −1.26766 −0.633828 0.773474i \(-0.718517\pi\)
−0.633828 + 0.773474i \(0.718517\pi\)
\(180\) 18.8599 1.40573
\(181\) 8.65716 0.643482 0.321741 0.946828i \(-0.395732\pi\)
0.321741 + 0.946828i \(0.395732\pi\)
\(182\) 1.80864 0.134065
\(183\) 16.0739 1.18821
\(184\) −43.7874 −3.22805
\(185\) 5.37633 0.395276
\(186\) −41.6300 −3.05246
\(187\) −1.00000 −0.0731272
\(188\) 12.3759 0.902604
\(189\) −9.18309 −0.667972
\(190\) 21.3793 1.55102
\(191\) −18.3254 −1.32598 −0.662989 0.748629i \(-0.730712\pi\)
−0.662989 + 0.748629i \(0.730712\pi\)
\(192\) 45.6044 3.29121
\(193\) 2.71391 0.195352 0.0976759 0.995218i \(-0.468859\pi\)
0.0976759 + 0.995218i \(0.468859\pi\)
\(194\) 16.7380 1.20172
\(195\) 0.417448 0.0298941
\(196\) 47.6892 3.40637
\(197\) −20.0277 −1.42692 −0.713458 0.700698i \(-0.752872\pi\)
−0.713458 + 0.700698i \(0.752872\pi\)
\(198\) 10.3330 0.734333
\(199\) 17.7250 1.25649 0.628244 0.778016i \(-0.283774\pi\)
0.628244 + 0.778016i \(0.283774\pi\)
\(200\) 34.3274 2.42731
\(201\) −11.1204 −0.784371
\(202\) −36.0715 −2.53798
\(203\) −35.7221 −2.50720
\(204\) 13.4585 0.942285
\(205\) −1.62375 −0.113408
\(206\) 52.4527 3.65456
\(207\) 20.2239 1.40566
\(208\) 2.03034 0.140779
\(209\) 8.43016 0.583126
\(210\) 26.8222 1.85091
\(211\) −6.59004 −0.453677 −0.226838 0.973932i \(-0.572839\pi\)
−0.226838 + 0.973932i \(0.572839\pi\)
\(212\) −40.2407 −2.76374
\(213\) −30.3436 −2.07911
\(214\) −40.0860 −2.74022
\(215\) 0.949400 0.0647485
\(216\) −19.0580 −1.29673
\(217\) −23.9986 −1.62913
\(218\) 48.7787 3.30371
\(219\) 13.0905 0.884574
\(220\) −4.87554 −0.328709
\(221\) 0.167776 0.0112858
\(222\) −39.6432 −2.66068
\(223\) 2.99779 0.200747 0.100373 0.994950i \(-0.467996\pi\)
0.100373 + 0.994950i \(0.467996\pi\)
\(224\) 62.8553 4.19970
\(225\) −15.8546 −1.05698
\(226\) 2.22125 0.147756
\(227\) −15.8023 −1.04883 −0.524416 0.851462i \(-0.675716\pi\)
−0.524416 + 0.851462i \(0.675716\pi\)
\(228\) −113.457 −7.51391
\(229\) −22.5758 −1.49185 −0.745926 0.666028i \(-0.767993\pi\)
−0.745926 + 0.666028i \(0.767993\pi\)
\(230\) −13.2588 −0.874262
\(231\) 10.5764 0.695873
\(232\) −74.1355 −4.86723
\(233\) −18.4714 −1.21010 −0.605051 0.796186i \(-0.706847\pi\)
−0.605051 + 0.796186i \(0.706847\pi\)
\(234\) −1.73363 −0.113331
\(235\) 2.28798 0.149251
\(236\) −46.6166 −3.03448
\(237\) 10.5803 0.687261
\(238\) 10.7801 0.698768
\(239\) −8.75515 −0.566323 −0.283162 0.959072i \(-0.591383\pi\)
−0.283162 + 0.959072i \(0.591383\pi\)
\(240\) 30.1101 1.94360
\(241\) 7.41689 0.477764 0.238882 0.971049i \(-0.423219\pi\)
0.238882 + 0.971049i \(0.423219\pi\)
\(242\) −2.67122 −0.171712
\(243\) −21.6109 −1.38634
\(244\) 31.4971 2.01639
\(245\) 8.81649 0.563265
\(246\) 11.9730 0.763369
\(247\) −1.41438 −0.0899948
\(248\) −49.8052 −3.16263
\(249\) −20.1768 −1.27865
\(250\) 23.0746 1.45937
\(251\) −7.83995 −0.494853 −0.247427 0.968907i \(-0.579585\pi\)
−0.247427 + 0.968907i \(0.579585\pi\)
\(252\) −80.1683 −5.05013
\(253\) −5.22814 −0.328691
\(254\) −26.7886 −1.68086
\(255\) 2.48813 0.155813
\(256\) 6.15416 0.384635
\(257\) −1.22987 −0.0767174 −0.0383587 0.999264i \(-0.512213\pi\)
−0.0383587 + 0.999264i \(0.512213\pi\)
\(258\) −7.00056 −0.435836
\(259\) −22.8533 −1.42004
\(260\) 0.818000 0.0507302
\(261\) 34.2406 2.11944
\(262\) 48.6710 3.00690
\(263\) 8.64291 0.532945 0.266472 0.963843i \(-0.414142\pi\)
0.266472 + 0.963843i \(0.414142\pi\)
\(264\) 21.9495 1.35090
\(265\) −7.43946 −0.457002
\(266\) −90.8777 −5.57207
\(267\) 8.86315 0.542416
\(268\) −21.7906 −1.33108
\(269\) −19.0649 −1.16241 −0.581203 0.813759i \(-0.697418\pi\)
−0.581203 + 0.813759i \(0.697418\pi\)
\(270\) −5.77079 −0.351199
\(271\) 1.05569 0.0641285 0.0320643 0.999486i \(-0.489792\pi\)
0.0320643 + 0.999486i \(0.489792\pi\)
\(272\) 12.1015 0.733760
\(273\) −1.77446 −0.107395
\(274\) 2.14763 0.129743
\(275\) 4.09864 0.247157
\(276\) 70.3631 4.23536
\(277\) −7.96483 −0.478560 −0.239280 0.970951i \(-0.576911\pi\)
−0.239280 + 0.970951i \(0.576911\pi\)
\(278\) 50.2881 3.01608
\(279\) 23.0033 1.37717
\(280\) 32.0895 1.91771
\(281\) −4.96841 −0.296391 −0.148195 0.988958i \(-0.547346\pi\)
−0.148195 + 0.988958i \(0.547346\pi\)
\(282\) −16.8708 −1.00464
\(283\) −20.8777 −1.24105 −0.620526 0.784186i \(-0.713081\pi\)
−0.620526 + 0.784186i \(0.713081\pi\)
\(284\) −59.4589 −3.52824
\(285\) −20.9753 −1.24247
\(286\) 0.448166 0.0265006
\(287\) 6.90211 0.407419
\(288\) −60.2485 −3.55017
\(289\) 1.00000 0.0588235
\(290\) −22.4483 −1.31821
\(291\) −16.4217 −0.962655
\(292\) 25.6511 1.50112
\(293\) −6.95187 −0.406133 −0.203066 0.979165i \(-0.565091\pi\)
−0.203066 + 0.979165i \(0.565091\pi\)
\(294\) −65.0099 −3.79145
\(295\) −8.61819 −0.501770
\(296\) −47.4283 −2.75672
\(297\) −2.27550 −0.132038
\(298\) −58.4993 −3.38877
\(299\) 0.877158 0.0507273
\(300\) −55.1616 −3.18476
\(301\) −4.03564 −0.232610
\(302\) 25.7923 1.48418
\(303\) 35.3898 2.03309
\(304\) −102.017 −5.85110
\(305\) 5.82298 0.333423
\(306\) −10.3330 −0.590697
\(307\) 22.5669 1.28796 0.643981 0.765041i \(-0.277282\pi\)
0.643981 + 0.765041i \(0.277282\pi\)
\(308\) 20.7246 1.18089
\(309\) −51.4615 −2.92755
\(310\) −15.0810 −0.856546
\(311\) −14.5578 −0.825500 −0.412750 0.910844i \(-0.635432\pi\)
−0.412750 + 0.910844i \(0.635432\pi\)
\(312\) −3.68260 −0.208486
\(313\) −3.55013 −0.200665 −0.100333 0.994954i \(-0.531991\pi\)
−0.100333 + 0.994954i \(0.531991\pi\)
\(314\) −42.8523 −2.41830
\(315\) −14.8210 −0.835070
\(316\) 20.7322 1.16628
\(317\) −30.2570 −1.69940 −0.849702 0.527263i \(-0.823218\pi\)
−0.849702 + 0.527263i \(0.823218\pi\)
\(318\) 54.8561 3.07617
\(319\) −8.85167 −0.495598
\(320\) 16.5208 0.923543
\(321\) 39.3285 2.19510
\(322\) 56.3597 3.14080
\(323\) −8.43016 −0.469067
\(324\) −28.9704 −1.60946
\(325\) −0.687654 −0.0381442
\(326\) −41.7187 −2.31058
\(327\) −47.8570 −2.64650
\(328\) 14.3242 0.790923
\(329\) −9.72556 −0.536188
\(330\) 6.64633 0.365868
\(331\) −16.7959 −0.923184 −0.461592 0.887092i \(-0.652722\pi\)
−0.461592 + 0.887092i \(0.652722\pi\)
\(332\) −39.5369 −2.16987
\(333\) 21.9055 1.20041
\(334\) −4.07696 −0.223081
\(335\) −4.02852 −0.220101
\(336\) −127.990 −6.98240
\(337\) 8.22214 0.447888 0.223944 0.974602i \(-0.428107\pi\)
0.223944 + 0.974602i \(0.428107\pi\)
\(338\) 34.6506 1.88474
\(339\) −2.17928 −0.118362
\(340\) 4.87554 0.264413
\(341\) −5.94666 −0.322030
\(342\) 87.1086 4.71029
\(343\) −9.22703 −0.498213
\(344\) −8.37532 −0.451567
\(345\) 13.0083 0.700343
\(346\) 29.2959 1.57496
\(347\) 8.49821 0.456208 0.228104 0.973637i \(-0.426747\pi\)
0.228104 + 0.973637i \(0.426747\pi\)
\(348\) 119.130 6.38606
\(349\) 27.7391 1.48484 0.742420 0.669934i \(-0.233678\pi\)
0.742420 + 0.669934i \(0.233678\pi\)
\(350\) −44.1836 −2.36171
\(351\) 0.381774 0.0203776
\(352\) 15.5751 0.830153
\(353\) −7.63207 −0.406214 −0.203107 0.979157i \(-0.565104\pi\)
−0.203107 + 0.979157i \(0.565104\pi\)
\(354\) 63.5476 3.37752
\(355\) −10.9924 −0.583416
\(356\) 17.3675 0.920478
\(357\) −10.5764 −0.559760
\(358\) 45.3040 2.39439
\(359\) −34.4022 −1.81568 −0.907839 0.419318i \(-0.862269\pi\)
−0.907839 + 0.419318i \(0.862269\pi\)
\(360\) −30.7586 −1.62112
\(361\) 52.0676 2.74040
\(362\) −23.1251 −1.21543
\(363\) 2.62074 0.137553
\(364\) −3.47709 −0.182249
\(365\) 4.74222 0.248219
\(366\) −42.9367 −2.24434
\(367\) 25.6282 1.33778 0.668891 0.743360i \(-0.266769\pi\)
0.668891 + 0.743360i \(0.266769\pi\)
\(368\) 63.2683 3.29809
\(369\) −6.61586 −0.344408
\(370\) −14.3613 −0.746610
\(371\) 31.6231 1.64179
\(372\) 80.0333 4.14953
\(373\) −35.5160 −1.83895 −0.919476 0.393147i \(-0.871386\pi\)
−0.919476 + 0.393147i \(0.871386\pi\)
\(374\) 2.67122 0.138125
\(375\) −22.6386 −1.16905
\(376\) −20.1838 −1.04090
\(377\) 1.48510 0.0764865
\(378\) 24.5300 1.26169
\(379\) −0.741015 −0.0380634 −0.0190317 0.999819i \(-0.506058\pi\)
−0.0190317 + 0.999819i \(0.506058\pi\)
\(380\) −41.1016 −2.10847
\(381\) 26.2823 1.34648
\(382\) 48.9511 2.50455
\(383\) −1.63497 −0.0835432 −0.0417716 0.999127i \(-0.513300\pi\)
−0.0417716 + 0.999127i \(0.513300\pi\)
\(384\) −40.1829 −2.05058
\(385\) 3.83144 0.195268
\(386\) −7.24945 −0.368987
\(387\) 3.86827 0.196635
\(388\) −32.1786 −1.63362
\(389\) −17.2922 −0.876747 −0.438373 0.898793i \(-0.644445\pi\)
−0.438373 + 0.898793i \(0.644445\pi\)
\(390\) −1.11510 −0.0564650
\(391\) 5.22814 0.264399
\(392\) −77.7764 −3.92830
\(393\) −47.7513 −2.40873
\(394\) 53.4984 2.69521
\(395\) 3.83285 0.192852
\(396\) −19.8651 −0.998258
\(397\) −6.13451 −0.307882 −0.153941 0.988080i \(-0.549197\pi\)
−0.153941 + 0.988080i \(0.549197\pi\)
\(398\) −47.3472 −2.37330
\(399\) 89.1603 4.46360
\(400\) −49.5996 −2.47998
\(401\) −4.41238 −0.220344 −0.110172 0.993913i \(-0.535140\pi\)
−0.110172 + 0.993913i \(0.535140\pi\)
\(402\) 29.7049 1.48155
\(403\) 0.997708 0.0496994
\(404\) 69.3472 3.45015
\(405\) −5.35586 −0.266135
\(406\) 95.4216 4.73569
\(407\) −5.66287 −0.280698
\(408\) −21.9495 −1.08666
\(409\) 3.56821 0.176437 0.0882184 0.996101i \(-0.471883\pi\)
0.0882184 + 0.996101i \(0.471883\pi\)
\(410\) 4.33738 0.214208
\(411\) −2.10704 −0.103933
\(412\) −100.840 −4.96803
\(413\) 36.6336 1.80262
\(414\) −54.0223 −2.65505
\(415\) −7.30934 −0.358801
\(416\) −2.61312 −0.128119
\(417\) −49.3378 −2.41608
\(418\) −22.5188 −1.10143
\(419\) −19.3093 −0.943320 −0.471660 0.881780i \(-0.656345\pi\)
−0.471660 + 0.881780i \(0.656345\pi\)
\(420\) −51.5655 −2.51614
\(421\) 21.6769 1.05647 0.528234 0.849099i \(-0.322854\pi\)
0.528234 + 0.849099i \(0.322854\pi\)
\(422\) 17.6034 0.856921
\(423\) 9.32221 0.453261
\(424\) 65.6286 3.18721
\(425\) −4.09864 −0.198813
\(426\) 81.0543 3.92709
\(427\) −24.7519 −1.19783
\(428\) 77.0651 3.72508
\(429\) −0.439697 −0.0212288
\(430\) −2.53605 −0.122299
\(431\) 34.1955 1.64714 0.823570 0.567215i \(-0.191979\pi\)
0.823570 + 0.567215i \(0.191979\pi\)
\(432\) 27.5369 1.32487
\(433\) 25.9097 1.24514 0.622570 0.782564i \(-0.286089\pi\)
0.622570 + 0.782564i \(0.286089\pi\)
\(434\) 64.1054 3.07716
\(435\) 22.0241 1.05597
\(436\) −93.7768 −4.49109
\(437\) −44.0741 −2.10835
\(438\) −34.9676 −1.67081
\(439\) −29.3524 −1.40091 −0.700456 0.713695i \(-0.747020\pi\)
−0.700456 + 0.713695i \(0.747020\pi\)
\(440\) 7.95152 0.379074
\(441\) 35.9222 1.71058
\(442\) −0.448166 −0.0213171
\(443\) −19.2972 −0.916838 −0.458419 0.888736i \(-0.651584\pi\)
−0.458419 + 0.888736i \(0.651584\pi\)
\(444\) 76.2139 3.61695
\(445\) 3.21080 0.152207
\(446\) −8.00774 −0.379177
\(447\) 57.3938 2.71463
\(448\) −70.2256 −3.31785
\(449\) 0.450571 0.0212637 0.0106319 0.999943i \(-0.496616\pi\)
0.0106319 + 0.999943i \(0.496616\pi\)
\(450\) 42.3511 1.99645
\(451\) 1.71029 0.0805344
\(452\) −4.27035 −0.200860
\(453\) −25.3049 −1.18893
\(454\) 42.2112 1.98107
\(455\) −0.642823 −0.0301360
\(456\) 185.038 8.66519
\(457\) 6.88978 0.322290 0.161145 0.986931i \(-0.448481\pi\)
0.161145 + 0.986931i \(0.448481\pi\)
\(458\) 60.3049 2.81786
\(459\) 2.27550 0.106211
\(460\) 25.4900 1.18848
\(461\) −4.39969 −0.204914 −0.102457 0.994737i \(-0.532670\pi\)
−0.102457 + 0.994737i \(0.532670\pi\)
\(462\) −28.2517 −1.31439
\(463\) 8.95224 0.416046 0.208023 0.978124i \(-0.433297\pi\)
0.208023 + 0.978124i \(0.433297\pi\)
\(464\) 107.118 4.97284
\(465\) 14.7961 0.686151
\(466\) 49.3411 2.28568
\(467\) 42.2207 1.95374 0.976870 0.213835i \(-0.0685954\pi\)
0.976870 + 0.213835i \(0.0685954\pi\)
\(468\) 3.33288 0.154063
\(469\) 17.1241 0.790719
\(470\) −6.11168 −0.281911
\(471\) 42.0425 1.93722
\(472\) 76.0270 3.49943
\(473\) −1.00000 −0.0459800
\(474\) −28.2621 −1.29812
\(475\) 34.5522 1.58536
\(476\) −20.7246 −0.949910
\(477\) −30.3116 −1.38787
\(478\) 23.3869 1.06969
\(479\) −25.7835 −1.17808 −0.589038 0.808105i \(-0.700493\pi\)
−0.589038 + 0.808105i \(0.700493\pi\)
\(480\) −38.7527 −1.76881
\(481\) 0.950094 0.0433206
\(482\) −19.8121 −0.902418
\(483\) −55.2947 −2.51600
\(484\) 5.13539 0.233427
\(485\) −5.94898 −0.270129
\(486\) 57.7274 2.61857
\(487\) −23.0585 −1.04488 −0.522439 0.852676i \(-0.674978\pi\)
−0.522439 + 0.852676i \(0.674978\pi\)
\(488\) −51.3686 −2.32535
\(489\) 40.9303 1.85093
\(490\) −23.5508 −1.06391
\(491\) 0.592782 0.0267519 0.0133759 0.999911i \(-0.495742\pi\)
0.0133759 + 0.999911i \(0.495742\pi\)
\(492\) −23.0180 −1.03773
\(493\) 8.85167 0.398659
\(494\) 3.77811 0.169985
\(495\) −3.67253 −0.165068
\(496\) 71.9635 3.23126
\(497\) 46.7257 2.09593
\(498\) 53.8966 2.41516
\(499\) −15.1449 −0.677980 −0.338990 0.940790i \(-0.610085\pi\)
−0.338990 + 0.940790i \(0.610085\pi\)
\(500\) −44.3608 −1.98388
\(501\) 3.99991 0.178703
\(502\) 20.9422 0.934697
\(503\) −14.0043 −0.624419 −0.312210 0.950013i \(-0.601069\pi\)
−0.312210 + 0.950013i \(0.601069\pi\)
\(504\) 130.746 5.82391
\(505\) 12.8205 0.570504
\(506\) 13.9655 0.620842
\(507\) −33.9958 −1.50981
\(508\) 51.5008 2.28498
\(509\) 7.75138 0.343574 0.171787 0.985134i \(-0.445046\pi\)
0.171787 + 0.985134i \(0.445046\pi\)
\(510\) −6.64633 −0.294304
\(511\) −20.1579 −0.891733
\(512\) 14.2262 0.628717
\(513\) −19.1828 −0.846942
\(514\) 3.28526 0.144907
\(515\) −18.6427 −0.821495
\(516\) 13.4585 0.592478
\(517\) −2.40992 −0.105988
\(518\) 61.0461 2.68221
\(519\) −28.7423 −1.26165
\(520\) −1.33408 −0.0585031
\(521\) 4.15859 0.182191 0.0910956 0.995842i \(-0.470963\pi\)
0.0910956 + 0.995842i \(0.470963\pi\)
\(522\) −91.4641 −4.00327
\(523\) −29.0024 −1.26819 −0.634094 0.773256i \(-0.718627\pi\)
−0.634094 + 0.773256i \(0.718627\pi\)
\(524\) −93.5697 −4.08761
\(525\) 43.3487 1.89189
\(526\) −23.0871 −1.00664
\(527\) 5.94666 0.259041
\(528\) −31.7148 −1.38021
\(529\) 4.33349 0.188412
\(530\) 19.8724 0.863202
\(531\) −35.1142 −1.52383
\(532\) 174.712 7.57471
\(533\) −0.286946 −0.0124290
\(534\) −23.6754 −1.02453
\(535\) 14.2473 0.615965
\(536\) 35.5384 1.53502
\(537\) −44.4479 −1.91807
\(538\) 50.9264 2.19559
\(539\) −9.28639 −0.399993
\(540\) 11.0943 0.477422
\(541\) −7.47108 −0.321207 −0.160604 0.987019i \(-0.551344\pi\)
−0.160604 + 0.987019i \(0.551344\pi\)
\(542\) −2.81997 −0.121128
\(543\) 22.6882 0.973642
\(544\) −15.5751 −0.667775
\(545\) −17.3369 −0.742630
\(546\) 4.73996 0.202852
\(547\) −15.6496 −0.669128 −0.334564 0.942373i \(-0.608589\pi\)
−0.334564 + 0.942373i \(0.608589\pi\)
\(548\) −4.12880 −0.176374
\(549\) 23.7254 1.01257
\(550\) −10.9484 −0.466839
\(551\) −74.6210 −3.17896
\(552\) −114.755 −4.88430
\(553\) −16.2924 −0.692823
\(554\) 21.2758 0.903921
\(555\) 14.0899 0.598085
\(556\) −96.6785 −4.10008
\(557\) 9.34255 0.395857 0.197928 0.980216i \(-0.436579\pi\)
0.197928 + 0.980216i \(0.436579\pi\)
\(558\) −61.4467 −2.60125
\(559\) 0.167776 0.00709617
\(560\) −46.3661 −1.95932
\(561\) −2.62074 −0.110648
\(562\) 13.2717 0.559833
\(563\) 16.4963 0.695236 0.347618 0.937636i \(-0.386991\pi\)
0.347618 + 0.937636i \(0.386991\pi\)
\(564\) 32.4339 1.36572
\(565\) −0.789475 −0.0332135
\(566\) 55.7689 2.34414
\(567\) 22.7663 0.956095
\(568\) 96.9716 4.06884
\(569\) 4.77889 0.200341 0.100171 0.994970i \(-0.468061\pi\)
0.100171 + 0.994970i \(0.468061\pi\)
\(570\) 56.0296 2.34682
\(571\) 36.5704 1.53043 0.765213 0.643778i \(-0.222634\pi\)
0.765213 + 0.643778i \(0.222634\pi\)
\(572\) −0.861596 −0.0360252
\(573\) −48.0260 −2.00632
\(574\) −18.4370 −0.769547
\(575\) −21.4283 −0.893621
\(576\) 67.3131 2.80471
\(577\) −26.2557 −1.09304 −0.546519 0.837447i \(-0.684047\pi\)
−0.546519 + 0.837447i \(0.684047\pi\)
\(578\) −2.67122 −0.111108
\(579\) 7.11245 0.295583
\(580\) 43.1567 1.79198
\(581\) 31.0700 1.28900
\(582\) 43.8658 1.81830
\(583\) 7.83596 0.324532
\(584\) −41.8344 −1.73112
\(585\) 0.616163 0.0254752
\(586\) 18.5699 0.767117
\(587\) 10.1219 0.417776 0.208888 0.977940i \(-0.433016\pi\)
0.208888 + 0.977940i \(0.433016\pi\)
\(588\) 124.981 5.15413
\(589\) −50.1313 −2.06563
\(590\) 23.0210 0.947761
\(591\) −52.4874 −2.15904
\(592\) 68.5291 2.81653
\(593\) 13.2856 0.545575 0.272787 0.962074i \(-0.412054\pi\)
0.272787 + 0.962074i \(0.412054\pi\)
\(594\) 6.07835 0.249398
\(595\) −3.83144 −0.157074
\(596\) 112.464 4.60672
\(597\) 46.4525 1.90117
\(598\) −2.34308 −0.0958156
\(599\) −35.6049 −1.45478 −0.727388 0.686227i \(-0.759266\pi\)
−0.727388 + 0.686227i \(0.759266\pi\)
\(600\) 89.9631 3.67273
\(601\) −5.60169 −0.228498 −0.114249 0.993452i \(-0.536446\pi\)
−0.114249 + 0.993452i \(0.536446\pi\)
\(602\) 10.7801 0.439363
\(603\) −16.4139 −0.668427
\(604\) −49.5856 −2.01761
\(605\) 0.949400 0.0385986
\(606\) −94.5339 −3.84018
\(607\) −34.1744 −1.38710 −0.693548 0.720410i \(-0.743954\pi\)
−0.693548 + 0.720410i \(0.743954\pi\)
\(608\) 131.300 5.32492
\(609\) −93.6184 −3.79361
\(610\) −15.5544 −0.629781
\(611\) 0.404327 0.0163573
\(612\) 19.8651 0.802998
\(613\) 18.7263 0.756348 0.378174 0.925735i \(-0.376552\pi\)
0.378174 + 0.925735i \(0.376552\pi\)
\(614\) −60.2811 −2.43275
\(615\) −4.25542 −0.171595
\(616\) −33.7998 −1.36183
\(617\) −24.0661 −0.968865 −0.484433 0.874829i \(-0.660974\pi\)
−0.484433 + 0.874829i \(0.660974\pi\)
\(618\) 137.465 5.52965
\(619\) 5.08877 0.204535 0.102267 0.994757i \(-0.467390\pi\)
0.102267 + 0.994757i \(0.467390\pi\)
\(620\) 28.9932 1.16440
\(621\) 11.8966 0.477396
\(622\) 38.8872 1.55923
\(623\) −13.6482 −0.546806
\(624\) 5.32099 0.213010
\(625\) 12.2920 0.491682
\(626\) 9.48317 0.379024
\(627\) 22.0932 0.882319
\(628\) 82.3833 3.28745
\(629\) 5.66287 0.225793
\(630\) 39.5901 1.57731
\(631\) 29.8693 1.18908 0.594539 0.804067i \(-0.297335\pi\)
0.594539 + 0.804067i \(0.297335\pi\)
\(632\) −33.8122 −1.34498
\(633\) −17.2708 −0.686451
\(634\) 80.8231 3.20989
\(635\) 9.52115 0.377835
\(636\) −105.460 −4.18178
\(637\) 1.55803 0.0617315
\(638\) 23.6447 0.936103
\(639\) −44.7878 −1.77178
\(640\) −14.5568 −0.575410
\(641\) −39.0237 −1.54134 −0.770672 0.637232i \(-0.780079\pi\)
−0.770672 + 0.637232i \(0.780079\pi\)
\(642\) −105.055 −4.14619
\(643\) −9.14378 −0.360595 −0.180298 0.983612i \(-0.557706\pi\)
−0.180298 + 0.983612i \(0.557706\pi\)
\(644\) −108.351 −4.26963
\(645\) 2.48813 0.0979700
\(646\) 22.5188 0.885989
\(647\) −4.33675 −0.170495 −0.0852477 0.996360i \(-0.527168\pi\)
−0.0852477 + 0.996360i \(0.527168\pi\)
\(648\) 47.2478 1.85607
\(649\) 9.07751 0.356323
\(650\) 1.83687 0.0720480
\(651\) −62.8940 −2.46501
\(652\) 80.2039 3.14103
\(653\) 6.98784 0.273455 0.136728 0.990609i \(-0.456342\pi\)
0.136728 + 0.990609i \(0.456342\pi\)
\(654\) 127.836 4.99879
\(655\) −17.2986 −0.675912
\(656\) −20.6970 −0.808084
\(657\) 19.3219 0.753818
\(658\) 25.9791 1.01277
\(659\) 32.3388 1.25974 0.629871 0.776700i \(-0.283108\pi\)
0.629871 + 0.776700i \(0.283108\pi\)
\(660\) −12.7775 −0.497364
\(661\) −37.6419 −1.46410 −0.732050 0.681251i \(-0.761436\pi\)
−0.732050 + 0.681251i \(0.761436\pi\)
\(662\) 44.8654 1.74374
\(663\) 0.439697 0.0170764
\(664\) 64.4807 2.50234
\(665\) 32.2996 1.25253
\(666\) −58.5143 −2.26738
\(667\) 46.2778 1.79188
\(668\) 7.83792 0.303258
\(669\) 7.85642 0.303747
\(670\) 10.7610 0.415735
\(671\) −6.13333 −0.236775
\(672\) 164.727 6.35449
\(673\) 28.4658 1.09728 0.548639 0.836060i \(-0.315146\pi\)
0.548639 + 0.836060i \(0.315146\pi\)
\(674\) −21.9631 −0.845987
\(675\) −9.32645 −0.358975
\(676\) −66.6156 −2.56214
\(677\) 9.69865 0.372749 0.186375 0.982479i \(-0.440326\pi\)
0.186375 + 0.982479i \(0.440326\pi\)
\(678\) 5.82133 0.223567
\(679\) 25.2875 0.970445
\(680\) −7.95152 −0.304927
\(681\) −41.4136 −1.58697
\(682\) 15.8848 0.608261
\(683\) 9.07541 0.347261 0.173630 0.984811i \(-0.444450\pi\)
0.173630 + 0.984811i \(0.444450\pi\)
\(684\) −167.466 −6.40321
\(685\) −0.763307 −0.0291645
\(686\) 24.6474 0.941041
\(687\) −59.1653 −2.25730
\(688\) 12.1015 0.461365
\(689\) −1.31469 −0.0500856
\(690\) −34.7480 −1.32283
\(691\) 41.2002 1.56733 0.783665 0.621184i \(-0.213348\pi\)
0.783665 + 0.621184i \(0.213348\pi\)
\(692\) −56.3212 −2.14101
\(693\) 15.6109 0.593010
\(694\) −22.7005 −0.861701
\(695\) −17.8733 −0.677974
\(696\) −194.290 −7.36453
\(697\) −1.71029 −0.0647818
\(698\) −74.0972 −2.80462
\(699\) −48.4087 −1.83099
\(700\) 84.9427 3.21053
\(701\) 10.0973 0.381368 0.190684 0.981651i \(-0.438929\pi\)
0.190684 + 0.981651i \(0.438929\pi\)
\(702\) −1.01980 −0.0384899
\(703\) −47.7389 −1.80051
\(704\) −17.4014 −0.655838
\(705\) 5.99619 0.225829
\(706\) 20.3869 0.767271
\(707\) −54.4963 −2.04955
\(708\) −122.170 −4.59142
\(709\) 11.6574 0.437804 0.218902 0.975747i \(-0.429752\pi\)
0.218902 + 0.975747i \(0.429752\pi\)
\(710\) 29.3631 1.10198
\(711\) 15.6167 0.585671
\(712\) −28.3247 −1.06151
\(713\) 31.0900 1.16433
\(714\) 28.2517 1.05729
\(715\) −0.159287 −0.00595698
\(716\) −87.0967 −3.25496
\(717\) −22.9449 −0.856895
\(718\) 91.8957 3.42952
\(719\) −36.3273 −1.35478 −0.677390 0.735624i \(-0.736889\pi\)
−0.677390 + 0.735624i \(0.736889\pi\)
\(720\) 44.4431 1.65630
\(721\) 79.2450 2.95124
\(722\) −139.084 −5.17616
\(723\) 19.4377 0.722897
\(724\) 44.4579 1.65227
\(725\) −36.2798 −1.34740
\(726\) −7.00056 −0.259815
\(727\) −15.6139 −0.579087 −0.289543 0.957165i \(-0.593503\pi\)
−0.289543 + 0.957165i \(0.593503\pi\)
\(728\) 5.67079 0.210173
\(729\) −39.7126 −1.47084
\(730\) −12.6675 −0.468845
\(731\) 1.00000 0.0369863
\(732\) 82.5456 3.05097
\(733\) −3.11550 −0.115073 −0.0575367 0.998343i \(-0.518325\pi\)
−0.0575367 + 0.998343i \(0.518325\pi\)
\(734\) −68.4585 −2.52685
\(735\) 23.1057 0.852267
\(736\) −81.4286 −3.00150
\(737\) 4.24323 0.156301
\(738\) 17.6724 0.650529
\(739\) 51.5071 1.89472 0.947359 0.320174i \(-0.103741\pi\)
0.947359 + 0.320174i \(0.103741\pi\)
\(740\) 27.6096 1.01495
\(741\) −3.70672 −0.136170
\(742\) −84.4721 −3.10107
\(743\) 50.6592 1.85851 0.929253 0.369444i \(-0.120452\pi\)
0.929253 + 0.369444i \(0.120452\pi\)
\(744\) −130.526 −4.78533
\(745\) 20.7917 0.761750
\(746\) 94.8710 3.47348
\(747\) −29.7814 −1.08964
\(748\) −5.13539 −0.187769
\(749\) −60.5615 −2.21287
\(750\) 60.4725 2.20815
\(751\) −22.8286 −0.833029 −0.416514 0.909129i \(-0.636748\pi\)
−0.416514 + 0.909129i \(0.636748\pi\)
\(752\) 29.1636 1.06349
\(753\) −20.5465 −0.748755
\(754\) −3.96702 −0.144470
\(755\) −9.16708 −0.333624
\(756\) −47.1588 −1.71515
\(757\) 41.9916 1.52621 0.763105 0.646275i \(-0.223674\pi\)
0.763105 + 0.646275i \(0.223674\pi\)
\(758\) 1.97941 0.0718954
\(759\) −13.7016 −0.497336
\(760\) 67.0326 2.43153
\(761\) 46.4945 1.68542 0.842711 0.538366i \(-0.180958\pi\)
0.842711 + 0.538366i \(0.180958\pi\)
\(762\) −70.2058 −2.54329
\(763\) 73.6943 2.66791
\(764\) −94.1081 −3.40471
\(765\) 3.67253 0.132781
\(766\) 4.36736 0.157799
\(767\) −1.52299 −0.0549920
\(768\) 16.1285 0.581985
\(769\) 9.22702 0.332735 0.166367 0.986064i \(-0.446796\pi\)
0.166367 + 0.986064i \(0.446796\pi\)
\(770\) −10.2346 −0.368829
\(771\) −3.22318 −0.116080
\(772\) 13.9370 0.501604
\(773\) 24.3518 0.875875 0.437937 0.899005i \(-0.355709\pi\)
0.437937 + 0.899005i \(0.355709\pi\)
\(774\) −10.3330 −0.371411
\(775\) −24.3732 −0.875512
\(776\) 52.4801 1.88393
\(777\) −59.8925 −2.14863
\(778\) 46.1911 1.65603
\(779\) 14.4180 0.516579
\(780\) 2.14376 0.0767590
\(781\) 11.5783 0.414303
\(782\) −13.9655 −0.499405
\(783\) 20.1420 0.719815
\(784\) 112.379 4.01354
\(785\) 15.2305 0.543600
\(786\) 127.554 4.54970
\(787\) −26.1069 −0.930609 −0.465304 0.885151i \(-0.654055\pi\)
−0.465304 + 0.885151i \(0.654055\pi\)
\(788\) −102.850 −3.66389
\(789\) 22.6508 0.806390
\(790\) −10.2384 −0.364265
\(791\) 3.35584 0.119320
\(792\) 32.3980 1.15121
\(793\) 1.02903 0.0365418
\(794\) 16.3866 0.581539
\(795\) −19.4969 −0.691483
\(796\) 91.0246 3.22628
\(797\) 54.5131 1.93095 0.965476 0.260493i \(-0.0838850\pi\)
0.965476 + 0.260493i \(0.0838850\pi\)
\(798\) −238.167 −8.43100
\(799\) 2.40992 0.0852568
\(800\) 63.8365 2.25696
\(801\) 13.0822 0.462237
\(802\) 11.7864 0.416193
\(803\) −4.99497 −0.176269
\(804\) −57.1076 −2.01403
\(805\) −20.0313 −0.706010
\(806\) −2.66509 −0.0938739
\(807\) −49.9640 −1.75882
\(808\) −113.098 −3.97878
\(809\) −33.3485 −1.17247 −0.586235 0.810141i \(-0.699390\pi\)
−0.586235 + 0.810141i \(0.699390\pi\)
\(810\) 14.3067 0.502685
\(811\) −22.8260 −0.801530 −0.400765 0.916181i \(-0.631256\pi\)
−0.400765 + 0.916181i \(0.631256\pi\)
\(812\) −183.447 −6.43774
\(813\) 2.76668 0.0970318
\(814\) 15.1267 0.530192
\(815\) 14.8276 0.519388
\(816\) 31.7148 1.11024
\(817\) −8.43016 −0.294934
\(818\) −9.53146 −0.333260
\(819\) −2.61914 −0.0915202
\(820\) −8.33859 −0.291196
\(821\) −48.9846 −1.70958 −0.854788 0.518978i \(-0.826313\pi\)
−0.854788 + 0.518978i \(0.826313\pi\)
\(822\) 5.62837 0.196312
\(823\) 45.9147 1.60049 0.800243 0.599676i \(-0.204704\pi\)
0.800243 + 0.599676i \(0.204704\pi\)
\(824\) 164.460 5.72924
\(825\) 10.7415 0.373970
\(826\) −97.8561 −3.40485
\(827\) −7.96108 −0.276834 −0.138417 0.990374i \(-0.544201\pi\)
−0.138417 + 0.990374i \(0.544201\pi\)
\(828\) 103.857 3.60930
\(829\) 10.8082 0.375386 0.187693 0.982228i \(-0.439899\pi\)
0.187693 + 0.982228i \(0.439899\pi\)
\(830\) 19.5248 0.677716
\(831\) −20.8737 −0.724101
\(832\) 2.91953 0.101217
\(833\) 9.28639 0.321754
\(834\) 131.792 4.56358
\(835\) 1.44903 0.0501456
\(836\) 43.2922 1.49729
\(837\) 13.5316 0.467722
\(838\) 51.5793 1.78178
\(839\) 10.8435 0.374357 0.187179 0.982326i \(-0.440066\pi\)
0.187179 + 0.982326i \(0.440066\pi\)
\(840\) 84.0981 2.90166
\(841\) 49.3520 1.70179
\(842\) −57.9037 −1.99549
\(843\) −13.0209 −0.448464
\(844\) −33.8424 −1.16490
\(845\) −12.3155 −0.423665
\(846\) −24.9016 −0.856136
\(847\) −4.03564 −0.138666
\(848\) −94.8267 −3.25636
\(849\) −54.7151 −1.87782
\(850\) 10.9484 0.375525
\(851\) 29.6063 1.01489
\(852\) −155.826 −5.33852
\(853\) 29.0348 0.994132 0.497066 0.867713i \(-0.334411\pi\)
0.497066 + 0.867713i \(0.334411\pi\)
\(854\) 66.1177 2.26250
\(855\) −30.9600 −1.05881
\(856\) −125.685 −4.29584
\(857\) −22.9067 −0.782479 −0.391240 0.920289i \(-0.627954\pi\)
−0.391240 + 0.920289i \(0.627954\pi\)
\(858\) 1.17453 0.0400977
\(859\) 50.8516 1.73503 0.867517 0.497408i \(-0.165715\pi\)
0.867517 + 0.497408i \(0.165715\pi\)
\(860\) 4.87554 0.166255
\(861\) 18.0886 0.616459
\(862\) −91.3436 −3.11117
\(863\) 53.3484 1.81600 0.908000 0.418969i \(-0.137609\pi\)
0.908000 + 0.418969i \(0.137609\pi\)
\(864\) −35.4410 −1.20573
\(865\) −10.4123 −0.354029
\(866\) −69.2103 −2.35186
\(867\) 2.62074 0.0890049
\(868\) −123.242 −4.18311
\(869\) −4.03713 −0.136950
\(870\) −58.8311 −1.99456
\(871\) −0.711912 −0.0241222
\(872\) 152.941 5.17922
\(873\) −24.2387 −0.820357
\(874\) 117.731 3.98232
\(875\) 34.8609 1.17851
\(876\) 67.2249 2.27132
\(877\) −3.72789 −0.125882 −0.0629409 0.998017i \(-0.520048\pi\)
−0.0629409 + 0.998017i \(0.520048\pi\)
\(878\) 78.4066 2.64609
\(879\) −18.2190 −0.614513
\(880\) −11.4892 −0.387299
\(881\) −12.4484 −0.419399 −0.209699 0.977766i \(-0.567249\pi\)
−0.209699 + 0.977766i \(0.567249\pi\)
\(882\) −95.9560 −3.23101
\(883\) 23.2800 0.783433 0.391716 0.920086i \(-0.371881\pi\)
0.391716 + 0.920086i \(0.371881\pi\)
\(884\) 0.861596 0.0289786
\(885\) −22.5860 −0.759220
\(886\) 51.5470 1.73176
\(887\) −18.0951 −0.607575 −0.303788 0.952740i \(-0.598251\pi\)
−0.303788 + 0.952740i \(0.598251\pi\)
\(888\) −124.297 −4.17114
\(889\) −40.4718 −1.35738
\(890\) −8.57675 −0.287493
\(891\) 5.64131 0.188991
\(892\) 15.3948 0.515457
\(893\) −20.3160 −0.679849
\(894\) −153.311 −5.12749
\(895\) −16.1019 −0.538227
\(896\) 61.8771 2.06717
\(897\) 2.29880 0.0767547
\(898\) −1.20357 −0.0401637
\(899\) 52.6379 1.75557
\(900\) −81.4198 −2.71399
\(901\) −7.83596 −0.261054
\(902\) −4.56855 −0.152116
\(903\) −10.5764 −0.351959
\(904\) 6.96451 0.231636
\(905\) 8.21911 0.273212
\(906\) 67.5950 2.24569
\(907\) 32.6032 1.08257 0.541286 0.840839i \(-0.317938\pi\)
0.541286 + 0.840839i \(0.317938\pi\)
\(908\) −81.1508 −2.69308
\(909\) 52.2362 1.73256
\(910\) 1.71712 0.0569220
\(911\) −16.7868 −0.556171 −0.278086 0.960556i \(-0.589700\pi\)
−0.278086 + 0.960556i \(0.589700\pi\)
\(912\) −267.361 −8.85321
\(913\) 7.69890 0.254796
\(914\) −18.4041 −0.608753
\(915\) 15.2605 0.504497
\(916\) −115.936 −3.83063
\(917\) 73.5315 2.42823
\(918\) −6.07835 −0.200615
\(919\) −18.7918 −0.619884 −0.309942 0.950755i \(-0.600310\pi\)
−0.309942 + 0.950755i \(0.600310\pi\)
\(920\) −41.5717 −1.37058
\(921\) 59.1420 1.94879
\(922\) 11.7525 0.387049
\(923\) −1.94256 −0.0639400
\(924\) 54.3137 1.78679
\(925\) −23.2101 −0.763142
\(926\) −23.9134 −0.785842
\(927\) −75.9584 −2.49480
\(928\) −137.865 −4.52565
\(929\) 3.05221 0.100140 0.0500698 0.998746i \(-0.484056\pi\)
0.0500698 + 0.998746i \(0.484056\pi\)
\(930\) −39.5235 −1.29603
\(931\) −78.2857 −2.56571
\(932\) −94.8580 −3.10718
\(933\) −38.1523 −1.24905
\(934\) −112.781 −3.69029
\(935\) −0.949400 −0.0310487
\(936\) −5.43560 −0.177668
\(937\) −46.5580 −1.52098 −0.760492 0.649347i \(-0.775042\pi\)
−0.760492 + 0.649347i \(0.775042\pi\)
\(938\) −45.7423 −1.49354
\(939\) −9.30396 −0.303623
\(940\) 11.7497 0.383232
\(941\) 6.32792 0.206284 0.103142 0.994667i \(-0.467110\pi\)
0.103142 + 0.994667i \(0.467110\pi\)
\(942\) −112.305 −3.65908
\(943\) −8.94164 −0.291180
\(944\) −109.851 −3.57536
\(945\) −8.71843 −0.283611
\(946\) 2.67122 0.0868487
\(947\) −44.3781 −1.44209 −0.721047 0.692886i \(-0.756339\pi\)
−0.721047 + 0.692886i \(0.756339\pi\)
\(948\) 54.3338 1.76468
\(949\) 0.838036 0.0272038
\(950\) −92.2963 −2.99449
\(951\) −79.2958 −2.57134
\(952\) 33.7998 1.09546
\(953\) −26.2801 −0.851296 −0.425648 0.904889i \(-0.639954\pi\)
−0.425648 + 0.904889i \(0.639954\pi\)
\(954\) 80.9687 2.62146
\(955\) −17.3981 −0.562990
\(956\) −44.9611 −1.45415
\(957\) −23.1979 −0.749882
\(958\) 68.8732 2.22519
\(959\) 3.24461 0.104774
\(960\) 43.2968 1.39740
\(961\) 4.36281 0.140736
\(962\) −2.53791 −0.0818254
\(963\) 58.0497 1.87063
\(964\) 38.0887 1.22675
\(965\) 2.57659 0.0829433
\(966\) 147.704 4.75230
\(967\) 42.2745 1.35946 0.679728 0.733465i \(-0.262098\pi\)
0.679728 + 0.733465i \(0.262098\pi\)
\(968\) −8.37532 −0.269193
\(969\) −22.0932 −0.709737
\(970\) 15.8910 0.510230
\(971\) −26.9582 −0.865129 −0.432564 0.901603i \(-0.642391\pi\)
−0.432564 + 0.901603i \(0.642391\pi\)
\(972\) −110.980 −3.55970
\(973\) 75.9746 2.43563
\(974\) 61.5941 1.97360
\(975\) −1.80216 −0.0577153
\(976\) 74.2224 2.37580
\(977\) 30.4031 0.972682 0.486341 0.873769i \(-0.338331\pi\)
0.486341 + 0.873769i \(0.338331\pi\)
\(978\) −109.334 −3.49611
\(979\) −3.38193 −0.108087
\(980\) 45.2762 1.44629
\(981\) −70.6379 −2.25530
\(982\) −1.58345 −0.0505299
\(983\) 30.5554 0.974566 0.487283 0.873244i \(-0.337988\pi\)
0.487283 + 0.873244i \(0.337988\pi\)
\(984\) 37.5400 1.19673
\(985\) −19.0143 −0.605847
\(986\) −23.6447 −0.753001
\(987\) −25.4881 −0.811297
\(988\) −7.26340 −0.231079
\(989\) 5.22814 0.166245
\(990\) 9.81013 0.311786
\(991\) −3.75012 −0.119127 −0.0595633 0.998225i \(-0.518971\pi\)
−0.0595633 + 0.998225i \(0.518971\pi\)
\(992\) −92.6196 −2.94068
\(993\) −44.0175 −1.39685
\(994\) −124.814 −3.95887
\(995\) 16.8281 0.533486
\(996\) −103.616 −3.28319
\(997\) 49.4156 1.56501 0.782504 0.622645i \(-0.213942\pi\)
0.782504 + 0.622645i \(0.213942\pi\)
\(998\) 40.4553 1.28059
\(999\) 12.8859 0.407690
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8041.2.a.g.1.4 69
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.g.1.4 69 1.1 even 1 trivial